Scalable Bayesian Approach for the Dina Q-Matrix Estimation Combining Stochastic Optimization and Variational...

Area of Science:

• Psychometrics
• Educational Measurement
• Statistical Modeling

Background:

• Diagnostic classification models (DCMs) assess respondent strengths and weaknesses using attribute information.
• Q-matrices define item-attribute relationships, but misspecification can reduce diagnostic accuracy.
• Existing Bayesian Q-matrix estimation methods are computationally infeasible for large-scale assessments.

Purpose of the Study:

• To develop a scalable Q-matrix estimation method for the Deterministic Inputs, Noisy "And" Gate (DINA) model.
• To address the limitations of current methods in large-scale educational assessments.
• To improve the accuracy and robustness of diagnostic classification.

Main Methods:

• Proposed a novel framework for Q-matrix estimation based on maximum marginal likelihood.
• Developed a scalable estimation algorithm using stochastic optimization and variational inference.
• Focused on the Deterministic Inputs, Noisy "And" Gate (DINA) model.

Main Results:

• The proposed method demonstrates high-speed computation.
• Achieved good accuracy in Q-matrix estimation.
• Showed robustness to initial value choices and hyperparameter settings.

Conclusions:

• The new algorithm is a valuable tool for estimating Q-matrices in large-scale assessments.
• It offers a computationally efficient and accurate alternative to existing methods.
• Enhances the reliability of diagnostic classification in complex testing environments.